You will learn
- Read a problem and find what is asked.
- Choose the operation for each step.
- Solve both steps in order.
- Check that the answer makes sense.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Read the problem and find the question.
- Solve one step, then the next.
- Choose add or subtract for each step.
- Check that the answer makes sense.
Words to know
One part of a problem.
Adding or subtracting.
The total of all.
What remains.
1. Discover: the busy stall
Ada has 45 mangoes. She sells 20, then buys 15 more. How many does she have now? Can you do it in one step?
2. Understand: two-step problems
Some problems need two steps. Read slowly and ask: what do I know? what do I need? which operation first?
Ada: 45 mangoes. Step 1: sell 20, 45 − 20 = 25. Step 2: buy 15, 25 + 15 = 40.
Draw a bar or write each step on its own line, then check if the answer makes sense.
Idea 1: Find the steps
A two-step problem needs two operations. Find what the problem asks, then solve one step at a time.
Idea 2: Choose the operation
“Altogether” and “more” mean add. “Left”, “gave away” and “spent” mean subtract.
Idea 3: An example
30 pencils, 12 used, 20 added. Step 1: 30 − 12 = 18. Step 2: 18 + 20 = 38.
Why two steps? The answer to step 1 is needed to do step 2.
3. Worked examples
Example 1 (I show you): Subtract then add
A box has 30 pencils. 12 are used and 20 are added. How many now?
- 30 − 12 = 18.
- 18 + 20 = 38.
Answer: 38
Example 2 (We do it together): Subtract twice
Kofi has 50 coins. He spends 15 and then 10. How many are left?
- 50 − 15 = 35.
- 35 − 10 = 25.
Answer: 25
Example 3 (You try): Find a part first
Mary has 24 beads. Tom has 18 more than Mary. How many altogether?
Show the steps and answer
- Tom has 24 + 18 = 42.
- Together: 24 + 42 = 66.
Answer: 66
Did you know?
Shopkeepers solve two-step problems all day: total the bill, then work out change.
Why this matters
Real problems have more than one step. Two-step problems prepare us for them.
4. Explore: two steps
You need paper and a pencil.
- Read: 30 pencils; 12 used; 20 added.
- Step 1: 30 − 12 = 18.
- Step 2: 18 + 20 = 38.
- Write a sentence for the answer.
Think about it: what did you notice?
There are 38 pencils.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The question asks ___.
- Step 1: ___.
- Step 2: ___.
- The answer is ___.
Guided practice
Question 1. Ada: 45 − 20 = ?
25.
Question 2. Then 25 + 15 = ?
40.
Question 3. How many steps did the problem need?
Two.
Independent practice
Level 1: Start
- 60 eggs, 18 broke, 25 more come. How many?
- 35 + 20, then give 15. How many?
- 100 sweets, 30 to Ada, 45 to Tom. How many left?
- Class A has 28. Class B has 5 more. How many in both?
- Write the two steps for 50 − 15 − 10.
Level 2: Grow
- 50 mangoes, 20 sold, 15 added. How many now?
- Ama has 30. Kofi has 12 more. How many together?
- 80 books, 35 lent, 20 returned. How many now?
Level 3: Stretch
- A shop has 150 oranges. It sells 60 in the morning and 45 in the afternoon. How many are left?
- Tom has 36 stickers. Ali has 14 more. How many in all?
- Sade says 45 + 30 − 20 = 35. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A box has 30 pencils. 12 are used and then 20 are added. How many now?
Show a sample answer
38 pencils.
Another one. A school has 120 pupils. 35 leave and 28 join. How many pupils now?
Show a sample answer
120 − 35 = 85, then 85 + 28 = 113
7. Common mistakes
Fix: Reread the question to see if more is asked.
Fix: Read the question again and ask: is there more to find?
Fix: Look for key words such as left and altogether.
8. Lesson summary and revision card
- I can read a problem and find the question.
- I can choose the operation for each step.
- I can solve both steps in order.
- I can check my answer.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Break it into steps.
- Write each step.
- Check the answer.
11. Next lesson
Next lesson: Equal groups. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- 30 pencils, 12 used, 20 added. How many now? [3 marks]
- Kofi has 50 coins. He spends 15 and 10. How many are left? [3 marks]
- Mary has 24 beads. Tom has 18 more than Mary. How many altogether? [3 marks]
- What does a two-step problem need? [1 mark]
- There are 120 boys and 135 girls. 50 leave. How many remain? [3 marks]
Total: 13 marks.
Marking guide and model answers
- 30 − 12 = 18 [1]; 18 + 20 [1] = 38 [1]
- 50 − 15 = 35 [1]; 35 − 10 [1] = 25 [1]
- Tom 24 + 18 = 42 [1]; 24 + 42 [1] = 66 [1]
- Two operations [1]
- 120 + 135 = 255 [1]; 255 − 50 [1] = 205 [1]
Score guide: 12 to 13 = secure. 8 to 11 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 45 mangoes, sell 20, buy 15. How many?
- 60 eggs, 18 broke, 25 added. How many?
- 35 + 20 then give 15. How many?
- 100 sweets, 30 and 45 given. How many left?
- Class A 28, Class B 5 more. Both?
- 40 + 25, then take away 15. What is the answer?
- 70 mangoes. 30 sold, then 10 sold. How many left?
- Ama has 15. Ben has 10 more. How many together?
- Write the two steps for 60 − 10 + 5.
- A shop had 200 oranges. It sold 75 and 60. How many are left?
Homework
Write your own two-step problem about a market. Ask a family member to solve it.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 45 mangoes, sell 20, buy 15. How many? | 40 | 2 |
| 60 eggs, 18 broke, 25 added. How many? | 67 | 2 |
| 35 + 20 then give 15. How many? | 40 | 2 |
| 100 sweets, 30 and 45 given. How many left? | 25 | 2 |
| Class A 28, Class B 5 more. Both? | 61 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 40; 2 67; 3 40; 4 25; 5 61.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 50; 7 30; 8 40; 9 60 − 10 = 50; 50 + 5 = 55; 10 65.
Independent practice answers. Level 1: 1 60 − 18 = 42, 42 + 25 = 67; 2 35 + 20 = 55, 55 − 15 = 40; 3 100 − 30 − 45 = 25; 4 B has 33, so 61 in both; 5 50 − 15 = 35, then 35 − 10 = 25. Level 2: 1 45; 2 72; 3 65. Level 3: 1 45; 2 86; 3 45 + 30 = 75 and 75 − 20 = 55..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Read a problem and find what is asked | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Choose the operation for each step | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Solve both steps in order | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Check that the answer makes sense | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Doing only one step. Reread the question to see if more is asked.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Act the story out with counters, one step at a time.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child solves word problems that need two steps. You do not need to be good at mathematics to help.
- Make up shop problems with two steps.
- Ask your child to say each step aloud.
- Check: does the answer make sense?
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: read a problem and find what is asked; choose the operation for each step; solve both steps in order; check that the answer makes sense.
Prerequisite knowledge. Lessons 1 to 8.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need paper and a pencil. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. What is asked? What is step 1? What is step 2? Does it make sense?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Doing only one step. Reread the question to see if more is asked.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 13-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Act the story out with counters, one step at a time. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
This lesson is based on the sources below, and no official endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 2 » Operations & Algebraic Thinking; Grade 2 » Number & Operations in Base Ten. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 2.OA.A.1 (one- and two-step word problems within 100); Cambridge Primary Mathematics Stage 2. These sources informed the lesson.